the first sentence options are all fine. We don't use a capital o in o'clock though.
If it is - this is incorrect. You have already told us that it isn't, so there is no doubt -'if' - here. You mean 'When it is'
The alarm will be rung or will be ringing.
'Ringing' gives us a sense of what will be happening at the moment of 12. It is a way of saying 'this is how you will know it is 12 o'clock'. It focuses on the sound of the bell.
'Rung' gives us the sense that there is an arrangement for the bell to be rung at 12. It is a way of saying 'this is the time the bell will be rung'. It focuses on the time.
I think most contexts would require 'rung'.